Showing papers on "Viscous fingering published in 2001"
TL;DR: In this paper, the authors investigated pattern formation of thin PMMA films during both hot embossing and demoulding of micro-and nanostructures and found that the self-assembly is strongly influenced by the size and shape of the stamp cavities.
Abstract: We have investigated pattern formation of thin PMMA films during both hot embossing and demoulding of micro- and nanostructures. During filling of the stamp cavities, compressive and capillary effects were observed, and under certain conditions periodic patterns with characteristic length scales formed. In unstructured stamp regions the form of these patterns is affected by local differences in the pressure. For structured stamps, the self-assembly is strongly influenced by the size and the shape of the stamp cavities. Rapid expansion of trapped air resulted in viscous fingering patterns and a dewetting behaviour of the polymer could be observed.
139 citations
TL;DR: In this article, numerical simulation results for the displacement of a drop in a porous medium are presented for the drop is surrounded by a more viscous fluid with which it is fully miscible and the simulations are based on a set of augmented Hele-Shaw equations that account for nonconventional, so-called Korteweg stresses resulting from locally steep concentration gradients.
Abstract: Numerical simulation results are presented for the displacement of a drop in a porous medium. The drop is surrounded by a more viscous fluid with which it is fully miscible. The simulations are based on a set of augmented Hele–Shaw equations that account for nonconventional, so-called Korteweg stresses resulting from locally steep concentration gradients. Globally, these stresses tend to stabilize the displacement. However, there are important distinctions between their action and the effects of surface tension in an immiscible flow. Since the Korteweg stresses depend on the concentration gradient field, the effective net force across the miscible interface region is not just a function of the drop’s geometry, but also of the velocity gradient tensor. Locally high strain at the leading edge of the drop generates steep concentration gradients and large Korteweg stresses. Around the rear of the drop, the diffusion layer is much thicker and the related stresses smaller. The drop is seen to form a tail, which can be explained based on a pressure balance argument similar to the one invoked to explain tail formation in Hele–Shaw flows with surfactant. The dependence of such flows on the Peclet number is complex, as steeper concentration gradients amplify the growth of the viscous fingering instability, while simultaneously generating larger stabilizing Korteweg forces.
56 citations
TL;DR: In this article, the effects of reactant concentrations on the characteristics of reactive miscible viscous fingering in a Hele-Shaw cell at low finger-growth velocity were studied both experimentally and theoretically.
Abstract: Effects of reactant concentrations on the characteristics of reactive miscible viscous fingering in a Hele-Shaw cell at low finger-growth velocity were studied both experimentally and theoretically. The product distribution varies with the variations in the initial reactant concentrations and depends on the location of a reaction zone. When the reaction zone is located in the more-viscous-liquid region the product concentrates at the fingertips, but when it is located in the less-viscous-liquid region, the product spreads in a relatively broad area inside the fingers. This significant difference in the reaction pattern resulting from variations in the reactant concentrations is caused by the large difference of molecular diffusivity in the two liquids, that is, of viscosity which is one of the important factors for viscous fingering. These results are confirmed theoretically by one-dimensional diffusive–reactive analysis.
45 citations
TL;DR: In this paper, the authors investigated the steady finger propagation and the problem of finger width selection in a long plane channel with two visco-plastic fluids separated by a sharp interface and showed that for a given fixed interface, chosen from a wide class of physically sensible interface shapes, there exists a unique solution.
Abstract: We study steady miscible displacements of two visco-plastic fluids in a long plane channel. If the yield stress of the displacing fluid is less than that of the displaced fluid, uniform static residual layers can be left attached to the walls of the channel as the displacement front propagates steadily. We investigate this steady finger propagation and the problem of finger width selection. The problem is fully two-dimensional, with the two fluids separated by a sharp interface. For a given fixed interface, chosen from a wide class of physically sensible interface shapes, we show that there exists a unique solution. As well as flexibility in the exact shape of the interface, the residual static layer thickness is also non-unique. Typically layer thicknesses h ∈ (h min , h max ) admit a physically sensible static layer solution, where h min and h max are easily computable functions of the dimensionless problem parameters. The dependency of h min and h max on the dimensionless problem parameters is explained and example solutions are computed for different static residual thick-nesses.
34 citations
TL;DR: A universal "density" formalism is explored to describe nonequilibrium growth processes, specifically, the immiscible viscous fingering in Hele-Shaw cells and proves an asymptotic equivalency of both the stochastic and deterministic mean-field DLA formulations to the classic Saffman-Taylor hydrodynamics in terms of an interface evolution.
Abstract: We explore a universal ``density'' formalism to describe nonequilibrium growth processes, specifically, the immiscible viscous fingering in Hele-Shaw cells (usually referred to as the Saffman-Taylor problem). For that we develop an alternative approach to the viscous fingering phenomena, whose basic concepts have been recently published in a Rapid Communication [Phys. Rev. E 63, 045305(R) (2001)]. This approach uses the diffusion-limited aggregation (DLA) paradigm as a core: we introduce a mean-field DLA generalization in stochastic and deterministic formulations. The stochastic model, a quasicontinuum DLA, simulates Monte Carlo patterns, which demonstrate a striking resemblance to natural Hele-Shaw fingers and, for steady-state growth regimes, follow precisely the Saffman-Taylor analytical solutions in channel and sector configurations. The relevant deterministic theory, a complete set of differential equations for a time development of density fields, is derived from that stochastic model. As a principal conclusion, we prove an asymptotic equivalency of both the stochastic and deterministic mean-field DLA formulations to the classic Saffman-Taylor hydrodynamics in terms of an interface evolution.
18 citations
TL;DR: In this paper, the growth and the structure of non-Newtonian viscous fingering in a rectangular Hele-Shaw cell was studied. But the authors focused on the growth of thin fingers from a wide finger tip.
Abstract: Non-Newtonian viscous fingering in a rectangular Hele-Shaw cell was studied. Compressed air was injected into the cell filled with a more viscous fluid. For the more viscous fluids, glycerin was used as a Newtonian fluid, and aqueous solutions of carboxymethylcellulose (CMC) and polyacrylamide (PAA) were used as non-Newtonian fluids. The growth and the structure of viscous fingers were analyzed. The shear-thinning viscosity of the polymer solutions made the 'shielding' effect strong. When the 'shielding' appeared strongly, the fingers formed a branched structure. In the PAA solution, the change in the finger pattern, a sudden growth of thin fingers from a wide finger-tip, was observed. It was supposed that stretch-thickening elongational viscosity and the shear-thinning viscosity were related to this phenomenon.
17 citations
TL;DR: In this paper, a detailed two-dimensional flow visualization study was performed to examine the dynamics of viscous fingering in miscible displacements, showing that the fractal dimension decreases with decreasing gravity number and increasing viscosity ratio.
Abstract: A detailed two-dimensional flow visualization study was performed to examine the dynamics of viscous fingering in miscible displacements. Detailed quantitative miscible displacement experiments using a microcomputer-based imaging workstation on a variety of oil recovery fluid systems were performed. The effect of two dimensionless scaling groups, namely gravity number and viscosity ratio, on the displacement behavior was investigated. Based on image analysis, the irregular fingering patterns of the flow visualization experiments were analyzed for fractal characteristics. Results indicate that the areal sweep efficiency of unstable miscible displacement follows a fractal scaling law with a fractal dimension and proportionality constant related to the gravity number and the viscosity ratio. The study shows that the fractal dimension decreases with decreasing gravity number and increasing viscosity ratio. This relationship was mapped by an artificial neural network model, which can be used to estimate the fractal dimension and the proportionality constant of miscible displacements as functions of the two scaling groups. These results have potential application in the mathematical modeling of unstable EOR displacements and in the scaling of laboratory displacements to field conditions.
17 citations
Journal Article•
TL;DR: In this article, the authors demonstrate that the morphology of finger-like patterns formed during viscous fingering in a Hele-Shaw cell during displacement of paraffin oil by aqueous solutions of the surfactant sodium dodecyl sulphate (SDS), is extremely sensitive to interfacial tension variation brought about by complexation of divalent cations with SDS.
Abstract: †‡ The study of the formation of finger -like patterns during displacement of a viscous fluid by a less vi scous one is of technological importance. The morphology of the viscous-finger patterns generated is a function of many parameters such as the flow rate, difference in viscosities of the two fluids and the interfacial tension. We demonstrate herein that the morphology of patterns formed during viscous fingering in a Hele-Shaw cell during displacement of paraffin oil by aqueous solutions of the surfactant sodium dodecyl sulphate (SDS), is extremely sensitive to interfacial tension variation brought about by complexation of divalent cations with the surfactant SDS. The variation in morphology of the patterns formed has been quantified by measuring the fractal dimensions of structures formed in a radial HeleShaw cell as well as the average finger width in a linear Hele-Shaw cell. This technique shows promise for studying other interfacial phenomena in chemi stry such as biorecognitio n as well as dynamic processes occurring at interfaces. THE displacement of a viscous fluid by a less viscous one leads to the formation of finger -like patterns known as ‘viscous fingers’ 1 . First observed by petroleum engineers during secondary oil recovery 2 , the study of the phenomenon of viscous fingering has application in a range of fundamental and industrially important pro blems such as fluid flow in porous media 3 , dendritic solidification 4 , combustion in two dimensions 5 and electrochemical deposition 6 , to name just a few. While considerable research effort has been directed at u nderstanding the various physical factors governing viscous fingering 7–10 , application of viscous fingering pattern formation to problems in chemistry has not been attempted with much seriousness 11 . This is especially su rprising given that the interfacial tension between the two fluids plays an important role in the evolution of the viscous-finger morphology 1a,8,9 and should thus
14 citations
TL;DR: Through detailed simulations of anisotropic fingering, it is demonstrated conclusively that no selection independent of the small-scale cutoff (macroscopic selection) occurs in this system, and ordered patterns are dynamically selected only for not too small surface tensions.
Abstract: We study the issue of the selection of viscous fingering patterns in the limit of small surface tension. Through detailed simulations of anisotropic fingering, we demonstrate conclusively that no selection independent of the small-scale cutoff (macroscopic selection) occurs in this system. Rather, the small-scale cutoff completely controls the pattern, even on short time scales, in accordance with the theory of microscopic solvability. We demonstrate that ordered patterns are dynamically selected only for not too small surface tensions. For extremely small surface tensions, the system exhibits chaotic behavior and no regular pattern is realized.
12 citations
TL;DR: The modified Darcy's law, where the constant Viscosity is replaced by the shear thinning viscosity, gives good agreement with the experiments, irrespective of the cell and the fluid.
Abstract: We study the effect of anisotropy of the Hele-Shaw cell on the viscous fingering instability in dilute polymer solutions with shear thinning. In isotropic cells, the tip-splitting instability is observed at the same pressure gradient for a fixed polymer concentration, whereas in anisotropic cells the side oscillation instability occurs at higher pressure gradient than the tip-splitting instability. Narrowing of the finger width in the isotropic cell is well correlated with the tip-splitting instability, whereas the finger width in the anisotropic cell is almost independent of the sample. The modified Darcy's law, where the constant viscosity is replaced by the shear thinning viscosity, gives good agreement with the experiments, irrespective of the cell and the fluid.
10 citations
TL;DR: A Monte Carlo mean-field scheme for the diffusion-limited aggregation (DLA) model is introduced in order to simulate processes of viscous fingering, and patterns obtained demonstrate a striking resemblance to natural shapes in Hele-Shaw cells.
Abstract: We introduce a Monte Carlo mean-field scheme for the diffusion-limited aggregation (DLA) model, in order to simulate processes of viscous fingering. The patterns obtained demonstrate a striking resemblance to natural shapes in Hele-Shaw cells, reproducing the Saffman-Taylor analytical solutions in the stable regime. The corresponding deterministic equations of the mean-field DLA scheme are derived and studied.
TL;DR: In this article, a 10 mm layer of glycerol, with surface tension 63.4 dyn/cm, was first spin-coated onto a cleaned 10 cm silicon wafer.
Abstract: The spreading of a surface active film on a liquid layer of higher surface tension is known to produce an unusual fingering instability. Calculations based on linear stability and transient growth analysis suggest that Marangoni and capillary stresses cause dramatic variations in film thickness. These variations resemble dendritic streamlets of liquid which undergo repeated branching. Despite the similarity to viscous fingering patterns, the physical mechanisms controlling flow and instability are quite different. In this experiment, a 10 mm layer of glycerol, with surface tension 63.4 dyn/cm, was first spin-coated onto a cleaned 10 cm silicon wafer. The wafer was raised toward a chromium-nickel wire ~142 mm diameter! which was stretched between two posts and positioned in the focal plane of a microscope fitted with a 540 nm bandpass filter. The wire was coated with a film of oleic acid. Since the surface tension of oleic acid is 32.5 dyn/cm, it spontaneously spread across the surface of the glycerol rapidly thinning the liquid layer. Figures ~a!–~f! depict various examples of plume or fingerlike patterns that form during the spreading process. The sequence of periodically spaced circular patterns shown in ~a!–~c! are droplets of oleic acid ~250 mm diameter! caused by a Rayleigh instability as the wire was lifted from the glycerol layer. Each photograph spans ;2.5 mm; the contour lines represent interference fringes. In ~e!, streamlets appear just ahead of the oleic drop in a region strongly thinned by the initial spreading front. The thinner the initial glycerol layer, the more ramified the spreading patterns which develop, as seen in ~f!. We are grateful to the National Science Foundation CAREER ~CTS-9624776! and POWRE programs ~CTS9973538!, the Princeton Center for Complex Materials ~DMR-9809483!, and Unilever Research for financial support of our ongoing studies on Marangoni driven flow.
TL;DR: In this article, the effect of cetyltrimethylammonium bromide concentration above the critical micelle concentration on the profile of aqueous films between an approaching squalene droplet and a hydrophobic silica surface was investigated using the technique of imaging reflectometry.
Abstract: The effect of cetyltrimethylammonium bromide concentration above the critical micelle concentration on the profile of aqueous films between an approaching squalene droplet and a hydrophobic silica surface is investigated using the technique of imaging reflectometry. Drainage through the film periphery was observed to display viscous fingering effects and occurred via dendritic channels. This is explained to result from a combination of viscosity and interfacial tension effects. To our knowledge, this is the first time behavior such as this has been observed in a system involving the approach of a droplet to a solid surface.
TL;DR: It is concluded that the lateral undulations are generated by successive relaxations between two limiting finger widths, and the change between these two selected pattern scales is mainly due to the change in the anisotropy.
Abstract: Viscous fingering of an air-nematic interface in a radial Hele-Shaw cell is studied when periodically switching on and off an electric field, which reorients the nematic and thus changes its viscosity, as well as the surface tension and its anisotropy (mainly enforced by a single groove in the cell). Undulations at the sides of the fingers are observed that correlate with the switching frequency and with tip oscillations that give maximal velocity to smallest curvatures. These lateral undulations appear to be decoupled from spontaneous (noise induced) side branching. It is concluded that the lateral undulations are generated by successive relaxations between two limiting finger widths. The change between these two selected pattern scales is mainly due to the change in the anisotropy. This scenario is confirmed by numerical simulations in the channel geometry, using a phase-field model for anisotropic viscous fingering.
TL;DR: Viscous fingering was observed by injecting colored water into a Hele-Shaw cell preliminarily filled with a glycerin-water solution as mentioned in this paper, which varied the viscosity ratio, the flow rate, the gap width, and the density ratio.
Abstract: Viscous fingering was observed by injecting colored water into a Hele-Shaw cell preliminarily filled with a glycerin-water solution. We varied the viscosity ratio, the flow rate, the gap width, and the density ratio. The Peclet number was higher than 105. Some of the experiments were performed in microgravity conditions (parabolic flights) in order to eliminate the gravity influence on pattern formation. The video shows peculiarities of fingering in microgravity conditions for a gap width of 1.2 mm. The first sequence of two experiments shows the influence of the viscosity ratio, which was decreased by a factor of 10 from the first to the second experiment. The next sequence shows the influence of the flow velocity, which was decreased by a factor of two between the first and second experiments in this sequence.
Journal Article•
TL;DR: This work studies negative streamers between planar electrodes in a simple deterministic continuum approximation and observes that, for sufficiently large fields, the streamer tip can split.
Abstract: Non-ionized media subject to strong fields can become locally ionized by penetration of finger-shaped streamers. We study negative streamers between planar electrodes in a simple deterministic continuum approximation. We observe that for sufficiently large fields, the streamer tip can split. This happens close to Firsov's limit of ``ideal conductivity''. Qualitatively the tip splitting is due to a Laplacian instability quite like in viscous fingering. For future quantitative analytical progress, our stability analysis of planar fronts identifies the screening length as a regularization mechanism.
01 Jan 2001
TL;DR: In this paper, the Saffman-Taylor or viscous fingering instability is considered and the width of the finger is determined by the capillary number Ca = ΔμU/γ which represents the ratio of viscous forces over capillary forces; Δe is the viscosity difference between the two fluids, U the finger velocity and γ the surface tension.
Abstract: When a less viscous fluid pushes a more viscous fluid in a Hele-Shaw cell, the interface between the two fluids develops an instability leading to the formation of fingerlike patterns, called viscous fingers. This is the so-called Saffman-Taylor or viscous fingering instability [1]. The width of these viscous fingers is, for Newtonian fluids, determined by the capillary number Ca = ΔμU/γ which represents the ratio of viscous forces over capillary forces; Δe is the viscosity difference between the two fluids, U the finger velocity and γ the surface tension. The viscous forces tend to narrow the finger, whereas the capillary forces tend to widen it: the width of the finger decreases with increasing finger velocity. Due to its relative simplicity the viscous fingering instability has received much attention as an archetype of pattern forming systems, both theoretically and experimentally [1, 2] and is by now well understood.
TL;DR: In this article, a model of random porous media degradation via several fluid displacing, freezing and thawing cycles is investigated, where the fluid transport is based on the deterministic method with dispersion effect.
Abstract: A model of random porous media degradation is investigated via several fluid displacing, freezing and thawing cycles. The fluid transport is based on the deterministic method with dispersion effect. Research shows that the topology and the geometry of the porous media have a strong effect on displacement processes. The distribution of throat size N(r) after displacement but before freezing damage shows that the major change, after successive cycles, happens at the throat radius r > 0.9. The distribution of velocities normal to the interface of viscous fingering in percolation cluster is also studied. When iterations n greater than or equal to 10, the scaling function distribution is very sharp.
TL;DR: In this paper, an asymmetric random walk of water in a globally disordered medium is modeled by an external, nonwhite, dichotomic noise, and the resulting random walk is described in terms of an effective Markovian master equation.
Abstract: The imbibition of water in oil in Hele-Shaw cells is described as an asymmetric random walk of water in a globally disordered medium. The disorder is modeled by an external, nonwhite, dichotomic noise, and the resulting random walk is described in terms of an effective Markovian master equation. The solution to this equation is given, and the mean-squared-displacement (MSD) of fluid particles in an effective ordered medium is calculated. This same quantity was also measured in squared cells with a fixed separation, where Soltrol 170 was displaced by twice-distilled water. The flow generated by spontaneous displacement of oil presented three sequential stages, each with a characteristic speed and advancing front structure. In the first and third stages viscous fingering was not detected, but in the intermediate development stage it was observed. From the recorded time evolution of the front, its average displacement speed and the MSD of water in oil as a function of time were determined. Imbibition of water shows an enhanced diffusion regime in the first stage where MSD varies with t2, without any external noise effect. This is followed by a simple diffusion behavior in an effective medium in the second stage, where the external noise effect is large. In the third stage Gaussian diffusion prevails again. Numerical regression techniques were used to determine the best values of model parameters that fit experimental values for different stages, so that the sum of squared errors between theoretical predictions and experimental measurements is minimized. Good agreement was found with average errors of 14.3%, 5.9% and 0.6%, respectively.
12 Jun 2001
TL;DR: In this article, the effects of pressure pulsing on laboratory SCAL measurements using an unconsolidated and consolidated sand, refined oils and y-ray in-situ saturation monitoring (ISSM) were investigated.
Abstract: This study investigated the effects of pressure pulsing on laboratory SCAL measurements using an unconsolidated and consolidated sand, refined oils and y-ray in-situ saturation monitoring (ISSM). Published literature presented at the 1999 European lOR Symposium has suggested that under pulsed flow conditions, Darcy's law may no longer be a valid description of single phase flow and that suppression of viscous fingering may allo lead to significant improvement in oil productivity.
TL;DR: In this article, a new computer model of viscous fingering in a porous medium is presented and the simulation results show that the VF pattern is in agreement with the experimental results.
Abstract: A new computer model of viscous fingering (VF) in a porous medium is presented. The simulation results show that the VF pattern is in agreement with the experimental results. The simulation on the sweep efficiency also agrees with experiment results. The surface fractal dimension as a function of viscous ratio is found.
01 Jan 2001
TL;DR: The use of a unifying mathematical formulation in different physical models of branching can serve as a basis to understand why so different problems share the same branching phenomenon as mentioned in this paper, which has already proven to have some universality throughout this book and has even shown in the present chapter how the whole dynamics of a problem including this branching phenomenon can be mapped onto a different one in some approximation.
Abstract: The phenomenon of branching has already proven to have some universality throughout this book. Misbah has even shown in the present chapter how the whole dynamics of a problem — including this branching phenomenon — can be mapped onto a different one in some approximation. In this spirit, the use of a unifying mathematical formulation in different physical models of branching can serve as a basis to understand why so different problems share the same branching phenomenon.
Journal Article•
TL;DR: In this paper, the effect of meso structure of porous media on the shape of seepage boundary is investigated based on the sandstone experiment in sandstone, and the DLA effect of evolution of SEBP boundary is analyzed.
Abstract: Many engineering problems are closely related to the shape of seepage.The classical seepage mechanics can not be used to investigate the effect of meso structure of porous media on the shape of seepage because it is based on the assumption of homogenous media.Based on the meso seepage experiment in sandstone,the effect of the meso structure of porous media on the shape of seepage boundary is investigated in the paper.And the DLA effect of evolution of seepage boundary is analyzed.The relationship between the seepage of uncompressible fluid described by the Darcy's Law and the Laplacian fractals is suggested theoretically.Moreover,the stochastic differential equation of seepage boundary is proposed and the mechanism of seepage evolution is analyzed.The stochastic approach is initially proved by the agreement of theoretical value with the experimental results.It is indicated that the complexity of seepage boundary is caused by the mutual influence of the average motion described by the Darcy's Law and the fluctuation factor determined by the meso structure of porous media.The reason for the DLA effect of seepage boundary is the inhomogenous spatial distribution of pores in porous media.The conclusion of the paper can also be used to analyze the viscous fingering phenomenon in the process of oil displacing by water.
TL;DR: In this article, a new porous media model with correlated sites-bonds has been constructed, taking into account both the pore and throat geometries, the viscous fingering (VF) in porous media has been investigated by using the standard over-relaxed Gauss-Seidel scheme.
Abstract: A new porous media model with correlated sites-bonds has been constructed. Taking into account both the pore and throat geometries, the viscous fingering (VF) in porous media has been investigated by using the standard over-relaxed Gauss-Seidel scheme. The simulation results show that the VF's structure varies with the correlation parameter epsilon and the viscous ratio M. The sweep efficiency epsilon decreases along with the increase of the correlation parameter E and the lattice size R-1s. The surface fractal D-s gradually increases as the correlation parameter epsilon increases, whatever the viscous ratio M is. Also, D-s gradually increases as M increases whatever epsilon is. This means that not only the viscosity ratio but also the topology and the geometry of the porous media have a strong effect on the displacement process, the VF's structure, the sweep efficiency and the surface pattern.
01 Jan 2001
TL;DR: In this article, the onset and propagation of viscous fingers during liquid-liquid displacement is considered to have severe engineering consequences, while little has been done to model the onset or propagation of a viscous finger.
Abstract: Viscous fingering is an extremely important phenomenon in enhanced oil recovery, drilling underground liquid waste disposal, and porous bed reactors. It takes place when the viscous forces of a displacing fluid have greater momentum than those of the displaced fluid. While the onset and propagation of viscous fingers during liquid-liquid displacement is considered to have severe engineering consequences, little has been done to model the onset and propagation of a viscous finger. This is especially true for viscous fingering under combined thermal and chemical convection in a rotating porous medium. This constituted the subject of the present investigation.